1459 12 archive 33 disk0/00/00/14/59 2007-12-17 05:07:10 2008-08-16 01:45:23 2007-12-17 05:07:10 article show Bracic, Janko janko.bracic@fmf.uni-lj.si Moslehian, Mohammad Sal moslehian@ferdowsi.um.ac.ir University of Ljubljana, Dept. of Mathematics Ferdowsi University, Dept. of Mathematics pub Q none 3-homomorphism, Homomorphism, Continuity, Banach algebra, Bounded approximate identity, Second dual, Arens regularity, C*-algebra. A linear map $\varphi : \mathcal{A} \rightarrow \mathcal{B}$ between (Banach) algebras is called 3- homomorphism if $\varphi (abc) = \varphi (a)\varphi (b)\varphi (c)$ for each $a, b, c \in \mathcal{A}$. We investigate 3-homomorphisms on Banach algebras with bounded approximate identities and establish in two ways (for unital and non-unital cases) that every involution preserving homomorphism between $C^\ast$-algebras is norm decreasing. 2007 published Bulletin of the Malaysian Mathematical Sciences Society 30 2 Penerbit Universiti Sains Malaysia 195-200 TRUE 0126-6705 http://math.usm.my/bulletin/pdf/v30n2/v30n2p10.pdf http://math.usm.my/bulletin/html/vol30_2_10.htm [1] H.G. Dales, Banach Algebras and Automatic Continuity, London Math. Soc. Monographs 24, Clarendon Press, Oxford, 2000. [2] L.A. Harris, A generalization of C*-algebras, Proc. Lond. Math. Soc. 42(3)(1981), 331-361. [3] S. Hejazian, M. Mirzavaziri and M.S. Moslehian, n-homomorphisms, Bull. Iranian Math. Soc. 31(1)(2005), 13—23.